Related papers: Reconstructing the system coefficients for coupled…
In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…
We present a method to probe the Out-of-Time-Order Correlators (OTOCs) of a general system by coupling it to a harmonic oscillator probe. When the system's degrees of freedom are traced out, the OTOCs imprint themselves on the generalized…
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods.…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled…
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…
In this work, we consider the linear inverse problem $y=Ax+\epsilon$, where $A\colon X\to Y$ is a known linear operator between the separable Hilbert spaces $X$ and $Y$, $x$ is a random variable in $X$ and $\epsilon$ is a zero-mean random…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
In this work, the problem of optimizing damper positions in vibrational systems is investigated. The objective is to determine the positions of external dampers in such a way that the influence of the input on the output is minimized. The…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…
We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic…
We present a new way to make Ising machines, i.e., using networks of coupled self-sustaining nonlinear oscillators. Our scheme is theoretically rooted in a novel result that establishes that the phase dynamics of coupled oscillator systems,…
We propose a novel dictionary learning add-on for existing approximation algorithms for spherical inverse problems such as the downward continuation of the gravitational potential. The Inverse Problem Matching Pursuit (IPMP) algorithms…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…